TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU

As robotics increasingly adopts GPU-based simulation and large-scale learning, traditional CPU-based Model Predictive Control (MPC) solvers have become a bottleneck. The authors sought to develop a solver that is not only fast enough for real-time control but also fully differentiable and expressive enough to handle the complex dynamics, constraints, and cost functions required for modern robotics applications.

TurboMPC is built using a co-designed JAX-CUDA implementation that leverages the GPU's parallel architecture. The solver uses Sequential Quadratic Programming (SQP) to handle non-linear optimal control problems. Within each SQP iteration, it employs an Alternating Direction Method of Multipliers (ADMM) scheme to solve the resulting quadratic programs. To ensure differentiability, the authors use implicit differentiation on the active-set KKT conditions, allowing the solver to be integrated into learning pipelines like Reinforcement Learning (RL) and Bayesian Optimization (BO). The implementation uses direct sparse factorization (via cuDSS) to maintain efficiency across both forward and backward passes.

TurboMPC demonstrates substantial performance gains, achieving up to 15x speedups over state-of-the-art CPU solvers and 58x over existing GPU-based differentiable solvers. The solver's scalability is highlighted by its ability to maintain control over planning horizons exceeding 8,000 knot points. In practical deployment on a full-scale vehicle, the authors used the solver's differentiability to perform batched, GPU-accelerated parameter tuning via Bayesian optimization, resulting in faster minimum-time racing performance compared to hand-tuned baselines.

By bridging the gap between high-performance optimization and GPU-accelerated learning, TurboMPC enables the use of sophisticated, constraint-aware control in large-scale robotics pipelines. Its ability to handle complex formulations—such as implicit integrators for stiff dynamics and slack variables for feasibility—makes it a versatile tool for both research and real-world deployment in challenging environments.